Three different bumps with similar names

Motor engineers use three terms that buyers often mix up. Cogging torque is the pull between the rotor’s permanent magnets and the steel teeth of the stator. It exists with the power off, depends only on rotor position, and averages to zero over a turn. As the magnets pass the slot openings, the magnetic resistance of the air gap changes, and the rotor is pulled toward preferred positions. Kollmorgen describes the result as uneven torque, jerky running at low speed, and a rotor that stops only at certain positions. Motors without iron in the armature, such as the coreless motors used in humanoid hands, have no cogging at all.

Torque ripple is the wider term: any periodic variation in output torque while the motor is energised. Besides cogging, it comes from a back-EMF that is not a perfect sine, from the current waveform the drive produces, and from errors in its current sensors. The motion-control industry association’s paper on these terms draws the line simply: cogging is an open-circuit effect, present with no power applied, while ripple appears only when the motor is energised. Detent torque is mostly a stepper-motor term for the same unpowered holding effect.

In a humanoid joint, a fourth source sits after the motor: the reducer. A strain-wave gear has a kinematic error whose main component repeats twice per wave-generator revolution. A cycloidal disk that is slightly out of balance shakes once per turn. These errors reach the limb as torque or position ripple, at frequencies tied to motor speed.

Why slot and pole counts matter

Cogging repeats every time the magnet pattern lines up with the tooth pattern in the same way. The number of such alignments per mechanical revolution is the least common multiple (LCM) of the slot count and the pole count. A high LCM means many small, partly cancelling pulls instead of a few strong ones, so it generally gives lower cogging. That is why most joint motors use fractional-slot designs, where slots per pole per phase is not a whole number. Zhu and co-authors showed in 2003 that a four-pole, six-slot machine had about half the cogging of a comparable 12-slot design, because only half the pole edges met slot openings at the same time.

Motor makers then tune the remaining cogging with the magnet arc (the same paper found a minimum near 0.68 of the pole pitch), skewed magnets or skewed stator stacks, and shaped slot openings. Each fix costs a little average torque or adds manufacturing steps. Frameless joint motors are typically high-pole-count designs: Kollmorgen’s TBM2G robot series uses 7 or 10 pole pairs depending on size, and CubeMars lists 14 pole pairs for its RO50 Lite and 21 for the RO100.

How big is it in real joint hardware?

Few actuator suppliers publish cogging, and those that do rarely say how they measured it. CubeMars is an exception for some frameless motors: the RO50 Lite lists 10 N·mm of cogging against 0.3 N·m rated and 0.9 N·m peak torque, and the larger RO100 KV55 lists 55 N·mm against 4 N·m rated and 12 N·m peak. Kollmorgen gives cogging for several housed servo families at ±1.5 to ±2 percent, without stating the base, and its TBM2G frameless robot motors are sold as a “low cogging design” with no figure.

At the joint output, the reducer adds its own ripple. UCLA researchers measured an average torque ripple of ±1.5 N·m on a 10:1 cycloidal quasi-direct-drive actuator rated at 37.5 N·m, and traced it to cycloid disk imbalance. For strain-wave gears, EPFL researchers fitted the kinematic error of a harmonic drive and found its dominant component at twice per wave-generator turn, with smaller components at higher even orders, and cited roughly a 20 percent change in error size over a 56 °C temperature span.

Why a humanoid cares about a few percent

An industrial servo running point-to-point barely notices cogging, which mainly shows up at the start and end of a move. A humanoid joint is used differently. Most legged and many humanoid joints estimate their output torque from motor current instead of a torque sensor, and they spend much of their time at low speed or holding still, where cogging is not smoothed out by rotor inertia. Every unmodelled bump becomes an error in the torque the joint thinks it is applying, and in the contact forces the controller infers from it.

Gear ratio multiplies the effect. Behind a 9:1 reducer, a 12-slot, 10-pole motor puts 540 cogging cycles into each output turn, and the cogging torque reaches the limb multiplied by the ratio, like any other motor torque. At walking speeds the frequency is high enough to be filtered by the structure, but during slow manipulation and standing balance it sits inside the control bandwidth. Torque ripple is also one source of the acoustic hum covered in our noise explainer, and one of the actuator effects that sim-to-real work has to cover, either with a learned actuator model or by training through randomised disturbances.

Fixing it in hardware and in software

Hardware fixes come first: fractional-slot combinations with a high LCM, optimised magnet arcs, skew and careful manufacturing tolerances. The software fix is a cogging map. The drive spins the motor slowly in both directions, records the current needed at each encoder position, and stores the position-dependent part as a lookup table. A US patent with a 2013 priority date describes exactly this for a robot actuator: the difference between the two directions cancels load and friction and leaves the cogging profile, which then becomes a feedforward term. Piccoli and Yim at the University of Pennsylvania used position-based characterisation on 11 low-cost brushless motors and removed an average of 69 percent of torque ripple without adding a force sensor.

The method is now a standard drive feature. The open-source ODrive controller runs an anticogging calibration that takes six minutes by default and adds the result as feedforward, with the warning that a poor position estimate can reduce stability margins. Kollmorgen’s S300 and S700 amplifiers include a cogging compensation function. Reducer ripple is harder to map because it changes with load and temperature, so research has turned to observers and learned models: the UCLA team’s recurrent network predicted the ripple amplitude of its cycloidal actuator to within 0.23 N·m on average and its frequency at 17.6 Hz against a measured 17.2 Hz.

What to ask an actuator supplier

• Cogging torque, with its base. Ask for a peak-to-peak figure in N·m and whether it is measured on the motor or at the joint output. A bare percentage without a reference torque cannot be compared.
• Slot and pole count. They tell you the cogging period and, through the gear ratio, the frequency the controller will see.
• Output torque ripple at low speed. Ripple measured at the output on a dynamometer includes the reducer, which is the number the robot actually feels.
• Compensation in the drive. Whether the drive stores a per-unit cogging map, how it is calibrated in production, and whether it survives a motor or encoder swap in the field.

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